算术教程（英文版） [A Course in Arithmetic] 下载 mobi epub pdf 电子书 2024

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内容简介

The first one is purely algebraic. Its objective is the classification ofquadratic forms over the field of rational numbers （Hasse-Minkowskitheorem）. It is achieved in Chapter IV. The first three chapters contain somepreliminaries： quadratic reciprocity law， p-adic fields， Hilbert symbols.Chapter V applies the preceding results to integral quadratic forms indiscriminant + 1. These forms occur in various questions： modular functions，differential topology， finite groups. The second part （Chapters VI and VII） uses "analytic" methods （holomor-phic functions）. Chapter VI gives the proof of the "theorem on arithmeticprogressions" due to Dirichlet; this theorem is used at a critical point in thefirst part （Chapter 111， no. 2.2）. Chapter VII deals with modular forms，and in particular， with theta functions. Some of the quadratic forms ofChapter V reappear here.

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目录

Preface
Part I-Algebraic Methods
ChapterI Finite fields
1-Generalities
2-Equations over a finite field
3-Quadratic reciprocity law
Appendix-Another proof of the quadratic reciprocity law
Chapter II p-adic fields
1-The ring Zp and the field
2-p-adic equations
3-The multiplicative group of
Chapter II nHilbert symbol
1-Local properties
2-Global properties
Chapter IV Quadratic forms over Qp and over Q
1-Quadratic forms
2-Quadratic forms over Q
3-Quadratic forms over Q
Appendix Sums of three squares
Chapter V Integral quadratic forms with discriminant
1-Preliminaries
2-Statement of results
3-Proofs
Part II-Analytic Methods
Chapter VI-The theorem on arithmetic progressions
1-Characters of finite abelian groups
2-Dirichlet series
3-Zeta function and L functions
4-Density and Dirichlet theorem
Chapter Vll-Modular forms
1-The modular group
2-Modular functions
3-The space of modular forms
4-Expansions at infinity
5-Hecke operators
6-Theta functions
Bibliography
Index of Definitions
Index of Notations

前言/序言

　　This book is divided into two parts.
　　The first one is purely algebraic. Its objective is the classification ofquadratic forms over the field of rational numbers （Hasse-Minkowskitheorem）. It is achieved in Chapter IV. The first three chapters contain somepreliminaries： quadratic reciprocity law， p-adic fields， Hilbert symbols.Chapter V applies the preceding results to integral quadratic forms indiscriminant + 1. These forms occur in various questions： modular functions，differential topology， finite groups.　 The second part （Chapters VI and VII） uses "analytic" methods （holomor-phic functions）. Chapter VI gives the proof of the "theorem on arithmeticprogressions" due to Dirichlet; this theorem is used at a critical point in thefirst part （Chapter 111， no. 2.2）. Chapter VII deals with modular forms，and in particular， with theta functions. Some of the quadratic forms ofChapter V reappear here.
　　The two parts correspond to lectures given in 1962 and 1964 to secondyear students at the Ecole Normale Superieure. A redaction of these lecturesin the form of duplicated notes， was made by J.-J. Saosuc （Chapters l-IV）and J.-P. Ramis and G. Ruget （Chapters VI-VIi）. They were very useful tome; I extend here my gratitude to their authors.

算术教程（英文版） [A Course in Arithmetic] 下载 mobi epub pdf txt 电子书 格式

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　　读者对象：数学专业的高年级本科生、研究生和相关专业的学者

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本书主要讲述具有一般系数体系拓扑空间的上同调理论。层论包括对代数拓扑很重要的领域。书中有好多创新点，引进不少新概念，全书内容贯穿一致。证实了广义同调空间中层理论上同调满足同调基本特性的事实。将相对上同调引入层理论中。

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法国著名数学家serre的经典之作，数论方面的初级教材，适合初学者

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　　读者对象：数学专业的高年级本科生、研究生和相关专业的学者本书主要讲述具有一般系数体系拓扑空间的上同调理论。层论包括对代数拓扑很重要的领域。书中有好多创新点，引进不少新概念，全书内容贯穿一致。证实了广义同调空间中层理论上同调满足同调基本特性的事实。将相对上同调引入层理论中。

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　　读者有一定的基本同调代数和代数拓扑知识就可以理解本书。每章末都附有练习，这些可以帮助学生更好的理解书中的知识体系。附录给出了部分习题的解答。第二版中在内容上做了较大的改动，增加了80多例子和大量更深层次的内容，如，Cech上同调、Oliver变换、插值理论、广义流形、局部齐性空间、同调纤维和p进变换群。目次：层和准层；层上同调；与其他上同调定理的比较；谱序列的应用；Borel-Moore同调；上层和ech同调。

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